Real 3-qubit gate decompositions via triality

Brendan Pawlowski

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arXiv · 2512.18049

Real 3-qubit gate decompositions via triality

Brendan Pawlowski

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Abstract

We show that any unimodular real 3-qubit gate can be expressed as the product of at most 14 CNOT gates plus single-qubit gates, improving on the bound of 16 CNOTs due to Wei and Di. Our method uses the exotic triality symmetry of $\operatorname{PSO}(8)$, and we explore some of the useful properties of this map in relation to the study of real 3-qubit gates.

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Brendan Pawlowski. 2025-12-19. Real 3-qubit gate decompositions via triality. https://arxiv.org/abs/2512.18049

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